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Regression model selection—a residual likelihood approach

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  • Peide Shi
  • Chih‐Ling Tsai

Abstract

Summary. We obtain the residual information criterion RIC, a selection criterion based on the residual log‐likelihood, for regression models including classical regression models, Box–Cox transformation models, weighted regression models and regression models with autoregressive moving average errors. We show that RIC is a consistent criterion, and that simulation studies for each of the four models indicate that RIC provides better model order choices than the Akaike information criterion, corrected Akaike information criterion, final prediction error, Cp and Radj2, except when the sample size is small and the signal‐to‐noise ratio is weak. In this case, none of the criteria performs well. Monte Carlo results also show that RIC is superior to the consistent Bayesian information criterion BIC when the signal‐to‐noise ratio is not weak, and it is comparable with BIC when the signal‐to‐noise ratio is weak and the sample size is large.

Suggested Citation

  • Peide Shi & Chih‐Ling Tsai, 2002. "Regression model selection—a residual likelihood approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 237-252, May.
  • Handle: RePEc:bla:jorssb:v:64:y:2002:i:2:p:237-252
    DOI: 10.1111/1467-9868.00335
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    1. Lahiri, Kajal & Egy, Daniel, 1981. "Joint estimation and testing for functional form and heteroskedasticity," Journal of Econometrics, Elsevier, vol. 15(2), pages 299-307, February.
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    2. Yuki Kawakubo & Tatsuya Kubokawa & Muni S. Srivastava, 2015. "A Variant of AIC Using Bayesian Marginal Likelihood," CIRJE F-Series CIRJE-F-971, CIRJE, Faculty of Economics, University of Tokyo.
    3. Cheng, Tsung-Chi, 2011. "Robust diagnostics for the heteroscedastic regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1845-1866, April.
    4. Zhao, Meng & Kulasekera, K.B., 2006. "Consistent linear model selection," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 520-530, March.
    5. Yuki Kawakubo & Tatsuya Kubokawa & Muni S. Srivastava, 2018. "A Variant of AIC Based on the Bayesian Marginal Likelihood," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 60-84, May.
    6. Hui Xiao & Yiguo Sun, 2020. "Forecasting the Returns of Cryptocurrency: A Model Averaging Approach," JRFM, MDPI, vol. 13(11), pages 1-15, November.
    7. Hui Xiao & Yiguo Sun, 2019. "On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study," JRFM, MDPI, vol. 12(3), pages 1-16, June.
    8. Azari, Rahman & Li, Lexin & Tsai, Chih-Ling, 2006. "Longitudinal data model selection," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3053-3066, July.
    9. Peter C.B. Phillips & Ye Chen, "undated". "Restricted Likelihood Ratio Tests in Predictive Regression," Cowles Foundation Discussion Papers 1968, Cowles Foundation for Research in Economics, Yale University.
    10. Arslan, Olcay, 2012. "Weighted LAD-LASSO method for robust parameter estimation and variable selection in regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1952-1965.
    11. Fábio Bayer & Francisco Cribari-Neto, 2015. "Bootstrap-based model selection criteria for beta regressions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 776-795, December.
    12. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    13. Miyashiro, Ryuhei & Takano, Yuichi, 2015. "Mixed integer second-order cone programming formulations for variable selection in linear regression," European Journal of Operational Research, Elsevier, vol. 247(3), pages 721-731.
    14. Girard, Stéphane & Lorenzo, Hadrien & Saracco, Jérôme, 2022. "Advanced topics in Sliced Inverse Regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    15. Kadriye Hilal Topal & Ebru Çağlayan Akay, 2020. "Hanehalkı Tüketim Harcamalarının Mikroekonometrik Analizi: LAD-LASSO Yöntemi," EKOIST Journal of Econometrics and Statistics, Istanbul University, Faculty of Economics, vol. 0(33), pages 13-31, December.
    16. Lexin Li & Xiangrong Yin, 2008. "Sliced Inverse Regression with Regularizations," Biometrics, The International Biometric Society, vol. 64(1), pages 124-131, March.

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